In this study, ?-interval valued set is defined whose elements are closed sub-intervals including ? of unit interval that I = [0, 1]. With different order relation on set, the properties examined. By help relation, it shown complete lattice. Negation function given in to study theoretical set. means discussions fundamental features studied. fuzzy sets defined. The algebraic these level subsets ...

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough...

In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets [36] and a soft sets [30]. Our ivn−soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft se...

A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $alpha$-level sets of fuzzy input-output data.Then,...

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

Type-2 fuzzy sets are growing in popularity as, for certain applications they model uncertainty and imprecision better than type1 fuzzy sets. However, type-2 fuzzy sets can be difficult to understand and explain. Recent work has introduced embedded type-2 fuzzy sets and the Representation Theorem which enable us to discuss type-2 fuzzy sets in a different way. In particular they allow for alter...